Fast Multibase Methods and Other Several Optimizations for Elliptic Curve Scalar Multiplication
Irvine Proceedings of the 12th International Conference on Practice and Theory in Public Key Cryptography: PKC '09
Novel Precomputation Schemes for Elliptic Curve Cryptosystems
ACNS '09 Proceedings of the 7th International Conference on Applied Cryptography and Network Security
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
Efficient precomputation schemes of kP+lQ
Information Processing Letters
Fast and scalable parallel processing of scalar multiplication in elliptic curve cryptosystems
Security and Communication Networks
Complete atomic blocks for elliptic curves in jacobian coordinates over prime fields
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
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We present an innovative methodology for accelerating the elliptic curve point formulae over prime fields. This flexible technique uses the substitution of multiplication with squaring and other cheaper operations, by exploiting the fact that field squaring is generally less costly than multiplication. Applying this substitution to the traditional formulae, we obtain faster point operations in unprotected sequential implementations. We show the significant impact our methodology has in protecting against Simple Side-Channel Attacks (SSCA). We modify the ECC point formulae to achieve a faster atomic structure when applying atomicity side-channel protection. In contrast to previous atomic operations that assumed squarings are undistinguishable from multiplications, our new atomic structure offers true SSCA-protection because it includes squaring in its formulation. We also extend our implementation to parallel architectures such as SIMD (Single-Instruction Multiple-Data). With the introduction of a new coordinate system and with the flexibility of our methodology, we present, to our knowledge, the fastest formulae for SIMD-based schemes that are capable of executing 3 and 4 operations simultaneously. Finally, a new parallel SSCA-protected scheme is proposed for multiprocessor/parallel architectures by applying the atomic structure presented in this work. Our parallel and atomic operations are shown to be significantly faster than previous implementations.